can someone correct these for me plz.
Simplify by combining like terms.
Problem#32
radical(63) minus 2radical(28) plus 5radical(7)
My answer: 4radical(7)
Find the perimeter of the triangle shown in the figure.
leg...1 = radical (5) + radical (3)
leg...2=radical (5) - radical (3)
Hypotenuse= 4
My answer: 4+2radical(5)
correct.
To simplify the expression, "radical(63) minus 2radical(28) plus 5radical(7)", you need to simplify each radical term separately and then combine like terms.
First, let's simplify radical(63). To do this, you can factor 63 into its prime factors: 3 x 3 x 7. Since there is no perfect square within these factors, you cannot simplify the square root any further.
Next, let's simplify 2radical(28). Similar to before, we factorize 28 into its prime factors: 2 x 2 x 7. Since 2 x 2 = 4 is a perfect square within these factors, we can simplify the square root of 28 to 2radical(7).
Lastly, simplify 5radical(7). Since 7 is a prime number, it cannot be simplified any further.
Now, let's combine the like terms in the expression: radical(63) - 2radical(28) + 5radical(7).
The simplified expression is: radical(63) - 2radical(28) + 5radical(7)
Plugging in the simplified values, we get: radical(63) - 2radical(28) + 5radical(7) = radical(3 x 3 x 7) - 2(2 x radical(7)) + 5radical(7).
This can be further simplified to: 3radical(7) - 4radical(7) + 5radical(7).
Combining the like terms, we obtain: 4radical(7).
So, the correct answer is indeed 4radical(7).
Moving on to the next problem, to find the perimeter of the triangle, we need to add up the lengths of all three sides.
The lengths of the legs are given as:
leg 1 = radical(5) + radical(3)
leg 2 = radical(5) - radical(3)
The length of the hypotenuse is given as 4.
To find the perimeter, add up all these lengths:
Perimeter = leg 1 + leg 2 + hypotenuse
Perimeter = (radical(5) + radical(3)) + (radical(5) - radical(3)) + 4
When you add the like terms (radical(5) and radical(3)) in leg 1 and leg 2, they cancel out each other:
Perimeter = 4 + 4
Simplifying further, we get:
Perimeter = 8
So, the correct answer for the perimeter of the triangle is 8.